Three Types of Chaos in the Forced Nonlinear Schrödinger Equation

Eli Shlizerman and Vered Rom-Kedar
Phys. Rev. Lett. 96, 024104 – Published 20 January 2006

Abstract

Three different types of chaotic behavior and instabilities (homoclinic chaos, hyperbolic resonance, and parabolic resonance) in Hamiltonian perturbations of the nonlinear Schrödinger (NLS) equation are described. The analysis is performed on a truncated model using a novel framework in which a hierarchy of bifurcations is constructed. It is demonstrated numerically that the forced NLS equation exhibits analogous types of chaotic phenomena. Thus, by adjusting the forcing frequency, the behavior near the plane wave solution may be set to any one of the three different types of chaos for any periodic box length.

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  • Received 25 September 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.024104

©2006 American Physical Society

Authors & Affiliations

Eli Shlizerman* and Vered Rom-Kedar

  • Weizmann Institute of Science, Israel

  • *Electronic address: eli.shlizerman@weizmann.ac.il
  • Electronic address: vered.rom-kedar@weizmann.ac.il

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Issue

Vol. 96, Iss. 2 — 20 January 2006

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